The theoretical development of statistical methodology is progressing in the areas of epidemiological models, multiple comparisons, survival analysis, and the design of experiments, each of which is applicable to longitudinal studies. The research utilizes various regression methods for prospective studies, Bayesian theory in conjunction with decision theory, and numerical computing methods. The methodology created provides original contributions to experimental testing associated with longitudinal studies, the simultaneous comparison of specified effects (e.g. treatments against a control or placebo), epidemiological study of disease states, survival or failure analysis of longitudinal data and other longitudinal observations representing growth, physical and mental disability, and other physical changes in humans and animals. The emphasis of this research is on the development of methods which yield cogent yet easily understood results when applied to data. The creative use of Bayesian therory in the area of multiple comparisons will fill a void in the established statistical armamentarium.